Question

Two rods are of same material and having same length and area. if heat $\Delta Q$ flows through them for $12$ min when they are joined side by side. If now both the rods are joined in parallel, then the some amount of heat $\Delta Q$ will flow in

• A. 24 min
• B. 3 min
• C. 12 min
• D. 6 min

Answer 1

The correct option is B 3 min

Let the thermal resistance of each rod $=R$
And temperature difference $=\theta$
When two rods are connected in series, effective thermal resistance $=2R$
Heat current flowing $=i=\frac{\theta }{2R}$
Which flows for 12 minutes.
$\Delta Q=12i=\frac{6\theta }{R}$
When the rods are in parallel the effective thermal resistance is $\frac{R}{2}$
i.e. heat flowing $=i_2=\frac{2\theta }{R}$
In 3 minutes it will flow $3i_2=\frac{6\theta }{R}=\Delta Q$
Hence the same heat will flow in 3 minutes.